PREDICTION OF HIGH-MOBILITY TWO-DIMENSIONAL ELECTRON GAS AT KTAO 3-BASED HETEROINTERFACES
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Chinese Physics B
PAPER
Prediction of high-mobility two-dimensional electron gas at KTaO3-based
heterointerfaces
To cite this article: Fu-Ning Wang et al 2019 Chinese Phys. B 28 047101
View the article online for updates and enhancements.
This content was downloaded from IP address 218.64.220.101 on 16/04/2019 at 14:23
Chin. Phys. B Vol. 28, No. 4 (2019) 047101
Prediction of high-mobility two-dimensional electron gas at
KTaO3-based heterointerfaces∗
Fu-Ning Wang(王芙凝), Ji-Chao Li(李吉超)† , Yi Li(李宜), Xin-Miao Zhang(张鑫淼),
Xue-Jin Wang(王学晋), Yu-Fei Chen(陈宇飞), Jian Liu(刘剑),
Chun-Lei Wang(王春雷), Ming-Lei Zhao(赵明磊), and Liang-Mo Mei(梅良模)
School of Physics, Shandong University, Jinan 250100, China
(Received 27 December 2018; revised manuscript received 13 February 2019; published online 5 March 2019)
First-principles calculations are performed to explore the possibility of generating the two-dimensional electron gas
(2DEG) at the interface between LaGaO3 /KTaO3 and NdGaO3 /KTaO3 (001) heterostructures. Two different models —
i.e., the superlattice model and the thin film model — are used to conduct a comprehensive investigation of the origin of
charge carriers. For the symmetric superlattice model, the LaGaO3 (or NdGaO3 ) film is nonpolar. The 2DEG with carrier
density on the order of 1014 cm−2 originates from the Ta dxy electrons contributed by both LaGaO3 (or NdGaO3 ) and
KTaO3 . For the thin film model, large polar distortions occur in the LaGaO3 and NdGaO3 layer, which entirely screens
the built-in electric field and prevents electrons from transferring to the interface. Electrons of KTaO3 are accumulated at
the interface, contributing to the formation of the 2DEG. All the heterostructures exhibit conducting properties regardless
of the film thickness. Compared with the Ti dxy electrons in SrTiO3 -based heterostructures, the Ta dxy electrons have small
effective mass and they are expected to move with higher mobility along the interface. These findings reveal the promising
applications of 2DEG in novel nanoelectronic devices.
Keywords: 2DEG, first-principles calculation, interface
PACS: 71.10.Ca, 63.20.dk, 67.30.hp DOI: 10.1088/1674-1056/28/4/047101
1. Introduction Although lots of STO-based heterostructures host high-
Oxide heterostructures have emerged as a powerful plat- density 2DEG, low room-temperature mobility (less than
form for discovering novel interfacial properties, such as 10 cm2 /V·s) [4,9,26,28,34] largely constrains their development
magnetism [1] and superconductivity. [2,3] One major area of and practical application in a general case. Compared with
interest within the field is the two-dimensional electron gas STO, KTaO3 (KTO) is also a widely used substrate material
(2DEG) discovered at the interface between two insulators: and its mobility at room temperature is 30 cm2 /V·s. [35] One
LaAlO3 (LAO) and SrTiO3 (STO). [4] The 2DEG with high could speculate that the mobility of the 2DEG in heterostruc-
sheet carrier density is particularly notable for its potential ap- tures based on KTO could be further improved. Zou et al. [36]
first observed the conducting interface in LTO/KTO. Sur-
plications in nanoelectronic devices. [5] The mechanism of for-
prisingly, the electron mobility in the LTO/KTO heterostruc-
mation of the 2DEG remains a primary concern and several
ture is as high as 21 cm2 /V·s at room temperature, sev-
theories have been proposed. Electronic reconstruction due
eral times larger than that of doped STO. Later the high-
to the polar discontinuity, [6–8] oxygen vacancies in STO, [9–12]
quality 2DEG has been observed at the amorphous LAO/KTO
and the cation intermixing across the interface [13,14] have been
heterointerface. [37] Recently, the epitaxial films of the EuO
considered to be responsible for the interfacial conductivity.
have also been successfully grown on KTO crystals by using
The origin of the 2DEG formed at the interface has been in-
the molecular beam epitaxy, and the 2DEG is observed with a
vestigated both in theory [15–18] and experiment. [9,19–24]
high mobility of 11.8 cm2 /V·s at room temperature. [38] In ad-
So far, most of the investigations of the 2DEG focus on
dition to experiments, it has been theoretically predicted that
the oxide heterostructures based on STO substrate, such as the
the 2DEG can be created at the interface of LAO/KTO. [39]
following
However, the 2DEG formed at the KTO-based heterointer-
LAO/STO, LaTiO3 /SrTiO3 (LTO/STO), [25,26] faces has been seldom studied in theory. Therefore, theoreti-
LaGaO3 /SrTiO3 (LGO/STO), [27] cal investigations on the new KTO-based heterostructures will
help to discover superior 2DEG system with higher mobility.
GdTiO3 /SrTiO3 (GTO/STO), [28]
In this article, a comprehensive study of LGO/KTO and
NdAlO3 /SrTiO3 (NAO/STO), [29] NGO/KTO heterostructures in two different models is car-
and NdGaO3 /SrTiO3 (NGO/STO). [30–33] ried out by using first-principles calculations to explore the
∗ Projectsupported by the National Basic Research Program of China (Grant No. 2013CB632506) and the National Natural Science Foundation of China (Grant
Nos. 11374186, 51231007, and 51202132).
† Corresponding author. E-mail: lijichao@sdu.edu.cn
© 2019 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn
047101-1
Chin. Phys. B Vol. 28, No. 4 (2019) 047101
possibility of generating the 2DEG at the interfaces. First, of AGO and 5.5 u.c. of KTO was studied. Owing to an
it is found that the 2DEG can be produced at LGO/KTO additional AO or TaO2 layer in AGO or KTO, there are
and NGO/KTO heterointerface in the symmetric superlattice two identical n-type interfaces. In the thin film model, an
model. The electrical properties are studied and the origin of (AGO)m /(KTO)6.5 /(AGO)m supercell consisting of 6.5 u.c. of
the 2DEG is discussed. Then, in the thin film model we find KTO and m u.c. of symmetric AGO film along the (001) di-
that the metallic properties of LGO/KTO and NGO/KTO het- rection was employed. 1 ≤ m ≤ 10 and m is an integer. To
erointerface are independent of the film thickness. The rea- minimize the interaction between neighboring surfaces, peri-
son why there is no transition from insulating to metallic for odic slabs were separated in the z direction by 15 Å of vacuum.
LGO/KTO nor NGO/KTO in the thin film model is explained The density functional theory calculations were performed by
and the stability of the interface is explored. using the projector augmented wave method as implemented
in the Vienna ab initio Simulation Package (VASP) [41] with
2. Models and computational details projector-augmented wave (PAW) potential. The electronic
For both LGO/KTO and NGO/KTO heterostructures, two exchange correlation potential was parameterized in the gen-
different models, i.e., the superlattice and the thin film model, eralized gradient approximation (GGA). [42] In all calculations
are used to investigate the geometrical and electronic struc- the plane wave energy cut-off was 400 eV and the reciprocal
tures, as shown in Fig. 1. Since it has been experimen- space was described by the Monkhorst–Pack scheme. [43] The
tally proven that the KO surface can be hardly obtained for in-plane lattice constants were fixed at the experimental lat-
(001) oriented KTO, [40] we only focus on the (AO)+ /(TaO2 )+ tice constant of bulk-KTO. The internal positions of the atoms
(A = La and Nd) interface. In the superlattice model, the were allowed to relax until the force acting on atoms was less
(AGO)5.5 /(KTO)5.5 superlattice containing 5.5 unit cells (u.c.) than 0.01 eV/Å.
(a)
b
O Ta Ga K La/Nd
c a
(b)
Fig. 1. Schematic illustration of different models in this study: (a) (AGO)5.5 /(KTO)5.5 (A = La or Nd) superlattices model and (b)
(AGO)6 /(KTO)6.5 /(AGO)6 supercell.
3. Results and discussion 3.874 Å [27] and 3.861 Å, [45] respectively. The lattice mis-
3.1. Bulk compounds match at the interface of LGO/KTO and NGO/KTO are 3.23%
and 3.58% respectively, comparable to that of PrAlO3 /SrTiO3
KTO has a cubic phase with space group Pm3̄m, and its
(3.41%) and NdAlO3 /SrTiO3 (3.61%), [46] which have been
experimental lattice constant is 3.989 Å. [44] In contrast, LGO experimentally prepared. In order to justify whether the 2DEG
and NGO both exhibit an orthorhombic phase, and they can can be formed at the interface of LGO/KTO and NGO/KTO,
be regarded as pseudocubic structures with lattice constant of the relative band alignment between the film oxides LGO and
10 KTO, and between film oxides NGO and KTO are calcu-
O 2s NGO
Ec lated by means of aligning their core energy levels of O 2s
5 orbitals. [46] As can be seen from Fig. 2, the conduction band
minimum (CBM) of LGO and NGO are both higher than that
DOS/(states/eV)
0
O 2s
of the KTO substrate, suggesting that the 2DEG will most
LGO
Ec
probably be formed and the electrons will be resident in the
5 KTO side.
0 3.2. Superlattice model
O 2s KTO
Ec To investigate the intrinsic properties of the interface,
5 the periodic superlattices are used due to no surface in
this model. The band structure of (LGO)5.5 /(KTO)5.5 and
0
-20 -10 0 10 (NGO)5.5 /(KTO)5.5 superlattice are obtained and shown in
Energy/eV Fig. 3. From Figs. 3(a) and 3(b), it is noted that some con-
Fig. 2. Calculated density of states of bulk KTO, LGO, and NGO, duction bands cross the Fermi level, indicating that both the
where O 2s energy level is aligned to locate CBM. superlattices are metallic. The band structure of NGO/KTO
047101-2Chin. Phys. B Vol. 28, No. 4 (2019) 047101
around the Fermi level is quite similar to that of LGO/KTO; vious studies, [36,39] indicating that the electron mobility can be
that is, the conduction bands’ bottom states of the superlat- improved by replacing STO substrate with KTO.
tices are mainly composed of Ta 5d orbitals. The light bands To investigate the spatial distribution of the electronic
which are parabolic in the 2D k space are occupied by Ta dxy states in more detail, the orbital-resolved partial density of
singlet, and the only one heavy band is occupied by Ta dxz/yz states (DOS) for Ta atoms of each layer in LGO/KTO surper-
doublet. To estimate the electron mobility, we calculate the lattice is obtained and plotted in Fig. 4. The analysis of band
electron effective mass (m∗ ) of the conduction band at the Γ
structure shows that the Ta 5d orbitals split into nondegenerate
point from the following equation:
dxy state and two-fold degenerate dxz/yz state. The 2DEG orig-
2 −1
∂ ε(k) inates from the dxy electrons at the interface while the dxz/yz
m∗ = }2 . (1)
∂ k2 state makes little contribution to the metallic characteristics
The m∗ is about 0.61me for the lower dxy band parallel to the with an interfacial carrier density (ns ) of 1.25 × 1014 cm−2 .
interface, while the m∗ is substantially larger (about 11.72me ) Compared with the small fraction of dxy states, the occupancy
for the upper dxz/yz band perpendicular to the interface. In of the dxz/yz band is dramatically enhanced in the interior of
contrast, for the LGO/STO and NGO/STO superlattice, the m∗ KTO. However, this band has quite a large electron effective
is 0.87me . [47,48] This implies that the electrons in KTO, with mass, and plays little part in the two-dimensional electric con-
smaller effective mass, can move with higher mobility along ductivity. The spatial distribution of the 2DEG for NGO/KTO
the interface. These results are in good agreement with the pre- superlattice is almost the same as that for LGO/KTO.
0.2 0.2
(a) (b)
0 0
-0.2 -0.2
Energy/eV
Energy/eV
-0.4 dxz/yz -0.4
11.72me
-0.6 -0.6
-0.8 -0.8
dxy
-1.0 -1.0
LGO/KTO 0.61me NGO/KTO
X Γ X X Γ X
Fig. 3. Conduction bands near Fermi energy for (a) (LGO)5.5 /(KTO)5.5 and (b) (NGO)5.5 /(KTO)5.5 superlattice, with vertical dashed line
indicating Fermi energy located at 0 eV.
1.50 1.50
Ta 6 (a) dxy Ta 6 (b) dxz/yz
0.75 0.75
0 0
Ta 5 Ta 5
PDOS/(states/eV)
PDOS/(states/eV)
Ta 4 Ta 4
Ta 3 Ta 3
Ta 2 Ta 2
Ta 1 Ta 1
-2 -1 0 1 2 -2 -1 0 1 2
Energy/eV Energy/eV
Fig. 4. Orbital-resolved partial DOS of (a) Ta dxy states and (b) Ta dxz/yz states of each layer for (LGO)5.5 /(KTO)5.5 . Ta 1 is the Ta atom at the
interface, Ta i is Ta atom of the i-th layer below it.
047101-3Chin. Phys. B Vol. 28, No. 4 (2019) 047101
superlattices are calculated, and shown in Fig. 5. It is obvious
0.3 (a) DZ/(Zi-ZO)
that there is a ferroelectric-like distortion of the oxygen octa-
Ta-O
0.2 K-O hedron on the KTO side; that is, oxygen ions move towards the
La-O interface while the cations move inward. And on the LGO (or
0.1 Ga-O
NGO) side, the relative displacements are quite small due to
DZ/A
0 no surface existing in the periodic superlattices. This behav-
-0.1 ior was also discovered in LAO/STO, [17] LGO/STO, [47] and
-0.2
NGO/STO [48] superlattices.
-0.3 KTO LGO 3.3. Thin film model
-8 -4 0 4 8
Layer The advantage of the thin film model is that the calculated
results compare well with the experimental observations by in-
0.3 (b) DZ/(Zi-ZO) troducing the polar field in the thin film. Generally, a threshold
Ta-O
0.2 K-O thickness of the thin film is needed to form the metallic inter-
Nd-O face for the oxide heterostructures with STO substrate, such
0.1 Ga-O
as LAO/STO, LGO/STO, and NGO/STO. In our calculations
DZ/A
0
it is noted that the LGO/KTO (or NGO/KTO) systems are all
-0.1 metallic when the thickness of LGO (or NGO) varies from
-0.2 1 u.c. to 10 u.c. Our calculations are in good agreement with
previous results about LAO/KTO, [39] indicating that there ex-
-0.3 KTO NGO
ists no such threshold thickness in KTO-based heterostructure.
-8 -4 0 4 8
Layer It is worth mentioning that Wang et al. found that there is an
overlap between the valence band maximum (VBM) and the
Fig. 5. Relative displacements of the cations and the oxygen anions in
each layer for (a) (LGO)5.5 /(KTO)5.5 and (b) (NGO)5.5 /(KTO)5.5 super- CBM for the LAO/KTO system when the thickness of LAO is
lattice along c axis. no less than 6 u.c. [39] However, such a behavior does not exist
The relative displacement between anion and cation in in our calculations, even when the thickness of LGO (or NGO)
each layer along the c axis of the LGO/KTO and NGO/KTO rises up to 10 u.c.
(a) (b)
2 2
(LGO)6
1 1
0 0
(LGO)5
(LGO)4
DOS/(states/eV)
(LGO)3
DOS/(states/eV)
(LGO)2
(LGO)1
(KTO)1
(KTO)2
(KTO)3
(KTO)4
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
Energy/eV Energy/eV
Fig. 6. Layer-projected partial DOS of (a) fully relaxed and (b) unrelaxed (LGO)6 /(KTO)6.5 /(LGO)6 heterostructure, along with the conducting
electron charge density from −1 eV to the Fermi level.
To understand the sources of this variation, the electronic Fig. 6(b), it is noted that the electrons contributed by LGO and
structure of relaxed and unrelaxed (AGO)6 /(KTO)6.5 /(AGO)6 KTO reside at the interface due to the polar discontinuity, re-
heterostructure are obtained. The layer-projected partial DOS sulting in the interfacial metallic states. In addition, the VBM
for the fully relaxed and unrelaxed (LGO)6 /(KTO)6.5 /(LGO)6 of each layer of LGO shifts towards the Fermi level as the dis-
system are compared as shown in Figs. 6(a) and 6(b). From tance to the interface increases. The hole conducting states
047101-4Chin. Phys. B Vol. 28, No. 4 (2019) 047101
are formed on the surface of GaO2 layer because electrons phenomenon was also found for NGO/STO system in our pre-
are transferred from the surface to the interface. In contrast, vious calculation. [48] However, the biggest difference between
even though there is also a shift of the VBM of each layer of NGO/STO and NGO/KTO heterointerface is that the former
LGO to higher energy for the optimized heterostructure, the keeps insulating while the latter shows conducting states. This
VBM of O 2p state does not cross the Fermi energy and no discrepancy can be explained by the fact that KTO plays a
charge transfer occurs. Accordingly, the LGO is insulating. role of electron donor. The electrons of KTO occupy the con-
These findings indicate that the LGO film of (LGO)6 /KTO duction bands of Ta dxy orbitals and form the 2DEG at the
heterostructure has a stronger polarization than the LAO film interface. As a result of the strong polarization, the interfacial
in (LAO)6 /KTO system mentioned before. This explains why carrier density of LGO/KTO and NGO/KTO in the thin film
there is no such overlapping between the VBM and the CBM model are both about an order of magnitude lower than that in
in our calculation. As shown in Fig. 7, the strong polariza- the superlattice model. An ns of 1013 cm−2 matches well with
tion in the NGO film greatly neutralizes the build-in electric that of LTO/KTO interface at 2 K, observed in experiment. [36]
field in the (NGO)6 /KTO system, and the NGO becomes in- Here the calculated m∗ is about 0.62me for the lowest Ta dxy
sulating, which is similar to the case of (LGO)6 /KTO. This band.
(a) (b)
2 2
(NGO)6
1 1
0 0
(NGO)5
(NGO)4
(NGO)3
DOS/(states/eV)
DOS/(states/eV)
(NGO)2
(NGO)1
(KTO)1
(KTO)2
(KTO)3
(KTO)4
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
Energy/eV Energy/eV
Fig. 7. Layer-projected partial DOS of (a) fully relaxed and (b) (NGO)6 /(KTO)6.5 /(NGO)6 heterostructure, along with the conducting electron
charge density from −1 eV to the Fermi level.
This analysis indicates that the lattice distortions have distortion is similar to that in (LGO)6 /KTO. In addition, for
a great influence on electrical properties. Figure 8 displays both of the KTO-based heterostructures the polarization in the
the relative displacements between anions and cations in each KTO layer is stronger than that in STO layer of STO-based
layer along the c axis of the relaxed heterostructures. Due to heterostructure.
the symmetry of the thin film model, only the relative displace- To quantify the polarization strength, the polarization P
ments in a half of the supercell are plotted. It is found that large within AGO film in AGO/KTO system is calculated from the
polar distortions do occur in both heterostructures. For the following equation: [50,51]
(LGO)6 /KTO system, the relative displacement in LaO layer N
e
increases from 0.25 Å to 0.33 Å with the increasing of the dis- P=
Ω ∑ Zm∗ δ zm , (2)
m=1
tance to the interface, while the relative displacement in GaO2
layer decreases from 0.18 Å to 0.08 Å. Comparing with the where N is the number of atoms in the unit cell, Ω is the vol-
(LGO)6 /STO system reported by Xu et al., [49] the polar distor- ume of the AGO film, δ zm is the relative displacement between
tion in LGO of LGO/KTO is strong. This could be ascribed to anion and cation in the m layer along the c axis. The calculated
the fact that the lattice mismatch of LGO/KTO is much larger values of born effective charge Zm∗ are 4.42, 3.21, −2.49, and
than that of LGO/STO (only 1%). For the (NGO)6 /KTO sys- −2.57 for La, Ga, and O ions in the LaO and GaO2 plane for
tem, the NdO layer is buckled to 0.27 Å–0.37 Å, and the GaO2 the LGO in the tetragonal phase, respectively. For the NGO
layer is buckled to 0.18 Å–0.08 Å. The magnitude of the polar in the tetragonal phase, the Zm∗ are 4.48, 3.19, −2.49, and
047101-5Chin. Phys. B Vol. 28, No. 4 (2019) 047101
−2.59 for Nd, Ga, and O ions in the NdO and GaO2 planes, in the heterostructure by replacing the other part with vac-
respectively. Figure 9 presents the polarization P of the AGO uum. The EHS represents the total energy of the heterostruc-
films for AGO/KTO heterostructures with different numbers ture, and A represents the interface area. The calculated cleav-
of AGO unit cells. Figure 9 clearly shows a trend of polariza- age energy for LGO/KTO and NGO/KTO are 0.33 eV/Å2
tion strength decreasing in the AGO film with the successive and 0.38 eV/Å2 respectively. Both values are larger than
increase of the AGO film thickness. For comparison, we also 0.11 eV/Å2 for LAO/KTO [39] and 0.19 eV/Å2 for LAO/STO
calculate the polarization P within LGO film for LGO/STO heterostructure. [52] This means that the interfacial cohesion of
system with 6 u.c. of LGO and 7 u.c. of LGO. This happens LGO/KTO and NGO/KTO is stronger. In other words, both of
because the LGO/STO heterointerface becomes metallic be- the heterointerfaces are theoretically stable and very likely to
yond a critical thickness of 7 u.c. of LGO in our calculation. be formed in experiment.
The resulting values are 45.26 µC/cm2 and 41.57 µC/cm2 for
100
(LGO)6 /STO and (LGO)7 /STO, respectively. It is thus tempt- LGO
90 NGO
ing to speculate that the critical LGO polarization is within
41.57 µC/cm2 –45.26 µC/cm2 . However, even when the thick- 80
P/mCScm-2
ness of LGO reaches 10 u.c. for LGO/KTO system, the cal- 70
culated polarization is as high as 46.49 µC/cm2 . Clearly, the
60
polarization of the LGO film is strong enough to totally coun-
teract the build-in electric field. For the NGO/KTO system, the 50
polarization of the NGO film is even stronger. The calculated 40
1 2 3 4 5 6 7 8 9 10
P is 51.93 µC/cm2 for the (NGO)10 /KTO heterostructure.
AGO unit cells
0.4
DZ/(Zi-ZO) (a) Fig. 9. Calculated polarization P in the AGO (A = La and Nd) films
Ta-O with respect to the AGO film thickness for the (AGO)m /KTO/(AGO)m
0.3
K-O (m = 1–10) heterostructures.
La-O
0.2 Ga-O
4. Conclusions
DZ/A
0.1
In this work, the possibility of generating the 2DEG
0
in two different models of LGO/KTO and NGO/KTO het-
-0.1 erostructure is explored by using first-principles density func-
-0.2 KTO
tional calculations. The 2DEG with a high carrier density of
LGO
1014 cm−2 is produced at LGO/KTO and NGO/KTO heteroin-
-6 -4 -2 0 2 4 6 8 10 12
Layer terface in the symmetric superlattice model. In the thin film
0.4 model, all the heterointerfaces are found to be metallic without
DZ/(Zi-ZO) (b)
Ta-O
an insulator-to-metal transition. The interfacial carrier density
0.3
K-O of the 2DEG is about an order of magnitude lower than that
Nd-O
0.2 Ga-O in the superlattice model because large polar distortions in the
DZ/A
0.1
LGO and NGO layers greatly screen the built-in electric field
and prevent electrons from transferring to the interface. The
0
partially filled Ta dxy orbital is the origin of the 2DEG. The Ta
-0.1 dxy electrons with smaller effective mass in KTO-based het-
erostructure are expected to move with higher mobility along
-0.2 KTO NGO
the interface. Our calculations are helpful in understanding
-6 -4 -2 0 2 4 6 8 10 12
Layer the 2DEG and have important implications for developing new
Fig. 8. Relative displacements of the cations and the oxygen anions heterostructure hosting superior 2DEG.
in each layer for panel (a) (LGO)6 /(KTO)6.5 /(LGO)6 and panel (b)
(NGO)6 /(KTO)6.5 /(NGO)6 heterostructure along the c axis.
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